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Polytope of Type {24,2,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,2,18}*1728
if this polytope has a name.
Group : SmallGroup(1728,15830)
Rank : 4
Schlafli Type : {24,2,18}
Number of vertices, edges, etc : 24, 24, 18, 18
Order of s0s1s2s3 : 72
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,2,9}*864, {12,2,18}*864
   3-fold quotients : {8,2,18}*576, {24,2,6}*576
   4-fold quotients : {12,2,9}*432, {6,2,18}*432
   6-fold quotients : {8,2,9}*288, {4,2,18}*288, {24,2,3}*288, {12,2,6}*288
   8-fold quotients : {3,2,18}*216, {6,2,9}*216
   9-fold quotients : {24,2,2}*192, {8,2,6}*192
   12-fold quotients : {4,2,9}*144, {2,2,18}*144, {12,2,3}*144, {6,2,6}*144
   16-fold quotients : {3,2,9}*108
   18-fold quotients : {8,2,3}*96, {12,2,2}*96, {4,2,6}*96
   24-fold quotients : {2,2,9}*72, {3,2,6}*72, {6,2,3}*72
   27-fold quotients : {8,2,2}*64
   36-fold quotients : {4,2,3}*48, {2,2,6}*48, {6,2,2}*48
   48-fold quotients : {3,2,3}*36
   54-fold quotients : {4,2,2}*32
   72-fold quotients : {2,2,3}*24, {3,2,2}*24
   108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,15)(13,17)(14,16)(19,22)(20,21)
(23,24);;
s1 := ( 1, 7)( 2, 4)( 3,13)( 5, 8)( 6,10)( 9,19)(11,14)(12,16)(15,23)(17,20)
(18,21)(22,24);;
s2 := (27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42);;
s3 := (25,29)(26,27)(28,33)(30,31)(32,37)(34,35)(36,41)(38,39)(40,42);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(42)!( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,15)(13,17)(14,16)(19,22)
(20,21)(23,24);
s1 := Sym(42)!( 1, 7)( 2, 4)( 3,13)( 5, 8)( 6,10)( 9,19)(11,14)(12,16)(15,23)
(17,20)(18,21)(22,24);
s2 := Sym(42)!(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42);
s3 := Sym(42)!(25,29)(26,27)(28,33)(30,31)(32,37)(34,35)(36,41)(38,39)(40,42);
poly := sub<Sym(42)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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